Markos Katsoulakis works in Applied Stochastic Analysis, Nonlinear Partial Differential Equations and Statistical Mechanics, focusing on the mathematical and computational aspects of phenomena with multiple, interrelating scales. He has extensively worked in interdisciplinary collaborations involving Mathematics, Chemical Engineering and lately in Atmospheric and Oceanic Sciences problems. His research work is primarily in (a) deterministic and stochastic mesoscopic modeling and simulation, (b) developing rigorous mathematical methods for the derivation of macroscopic laws from microscopic stochastic models, and (c) studying relaxation mechanisms in hyperbolic conservation laws and discrete velocity kinetic models. He is currently the Director for the Center of Applied Mathematics at the University of Massachusetts and he is an Associate Editor of SIAM Journal of Mathematical Analysis.
Articles
Hybrid deterministic stochastic systems with microscopic look-ahead dynamics (with AJ Majda and A Sopasakis), Communications in Mathematical Sciences (2010)
We study the impact of stochastic mechanisms on a coupled hybrid system consisting of a...
A Comparison Principle for Hamilton-Jacobi Equations Related to Controlled Gradient Flows in Infinite Dimensions (with J Feng), Archive for Rational Mechanics and Analysis (2009)
We develop new comparison principles for viscosity solutions of Hamilton–Jacobi equations associated with controlled gradient...
Coarse-Grained Langevin Approximations and Spatiotemporal Acceleration for Kinetic Monte Carlo Simulations of Diffusion of Interacting Particles (with S Are and A Szepessy), Chinese Annals of Mathematics Series B (2009)
Kinetic Monte Carlo methods provide a powerful computational tool for the simulation of microscopic processes...
Mathematical strategies in the coarse-graining of extensive systems: Error quantification and adaptivity (with P Plechac, L Rey-Bellet, and DK Tsagkarogiannis), Journal of Non-Newtonian Fluid Mechanics (2008)
In this paper we continue our study of coarse-graining schemes for stochastic many-body microscopic models...
Multibody interactions in coarse-graining schemes for extended systems (with S Are, P Plechac, and L Rey-Bellet), Siam Journal of Scientific Computing (2008)
In this paper we address the role of multibody interactions for the coarse-grained approximation of...
Other
Coarse-graining schemes for stochastic lattice systems with short and long-range interactions (with P Plechac, L Rey-Bellet, and D Tsagkarogiannis), Mathematics and Statistics Department Faculty Publication Series (2010)
We develop coarse-graining schemes for stochastic many-particle microscopic models with competing short- and long-range interactions...
Coupled coarse graining and Markov Chain Monte Carlo for lattice systems (with E Kalligiannaki and P Plechac), Mathematics and Statistics Department Faculty Publication Series (2010)
We propose an efficient Markov Chain Monte Carlo method for sampling
equilibrium distributions for stochastic lattice...
Deterministic Equations for Stochastic Spatial Evolutionary Games (with SH Hwang and L Rey-Bellet), Mathematics and Statistics Department Faculty Publication Series (2010)
In this paper we investigate the approximation properties of the coarse-graining procedure applied to kinetic...
Error Analysis of Coarse-Grained Kinetic Monte Carlo method (with P Plechac and A Sopasakis), Mathematics and Statistics Department Faculty Publication Series (2005)
In this paper we investigate the approximation properties of the coarse-graining procedure applied to kinetic...
Statistical equilibrium measures in micromagnetics (with P Plechac), Mathematics and Statistics Department Faculty Publication Series (2001)
We derive an equilibrium statistical theory for the macroscopic description of a ferromagnetic material at...